My DD is 3 years old, she has a speech delay which leads to an obvious communication frustrations. By DH and I work full time and we have struggled with getting her around other children her age since we don't know anyone with children her age. During the day she stays with my MIL. I joined a group on Facebook for local moms and I did have a meetup with one mom but it was a little awkward because her child was so much farther along than mine (and younger too) and my DD doesn't know how to interact with kids. She more or less just gets super excited and screams at them or laughs. We also tried daycare with her and that didn't work out (there is another post on her about that ordeal). We take her to the park where other kids are playing but it's pretty similar to what I just mentioned she gets really excited and screams which scares the other kids away

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I guess I'm just not sure how to teach her how to interact with kids. I've been telling her if she wants to play with the kids she needs to say "Hi" first not just run at them screaming. At home she plays nice with us, brings us toys to play with asks for "help" or "more" (the action words she says consistently) but around other kids she seems unsure of how to approach them, any advice?
Re: Socializing DD - How do I do it?
That was my son at age 3. He was still speech delayed (he has ASD) and even though he could speak he had trouble knowing what to say. So if he saw another little boy he'd like he'd run up to him and get really close and giggle hysterically. Sometimes if the other little kid was immature himself, or just really excited, it might touch off a game of tag, but other times, especially with girls, they'd be really turned off and turn the opposite direction. My son has always been in full-time daycare and his social delay is what prompted us to find a special needs inclusion daycare where he was with both typical peers and atypical peers with staff who is trained to prompt DS gently to get him to play "properly." At age three there wasn't much that he was able to do by himself other than playing "tag" or "chase". TBH- we didn't do any playdates at this age because they were really difficult. I don't think we did many at age 4 either. I remember we tried having neighbors over to play in our backyard and DS was very uninterested and I literally had to lock the house doors to keep him in the backyard. You may have luck with a social skills group where there is guided play. Fo us, he just had to mature to the point where he could understand the give and take of "playing". DS had a breakthrough the summer he was 5 where he really wanted to have kids over and actually engage with them.
ABA can provide a social skills group, too. We had the option to do it but turned it down because DS goes to daycare and he develops social skills with mainstreamed kids. I don't know where else you can find a social skills group.
I would continue the search for a daycare that can work with your daughter.
The clinic where we received speech therapy offered a social skills group. They couch it in terms of a "friends" group. Sometimes they would meet in a public place (like a zoo or playground), othertimes it was more therapy play-based at the clinic. It was only 1 hour a week and I think geared towards older kids.
DS received more intensive social skills in a classroom setting, about 10 hours a week. This was offered by his inclusion preschool and was run by his ST, OT, and ASD-trained preschool teacher. They followed a formal social skills curriculum (Michelle Garcia Winner) and had just 6 kids in the class so they were very closely monitored and prompted. This is really key- even in his inclusion preschool class 9 times out of 10 when I picked him up he'd be off playing with an aide or teacher and ignoring the other kids. It takes some diligent, trained professionals to keep him engaged properly with other children.
While I certainly saw a lot of gains with DS attending all these therapies, for us, it really seemed to be a lot about maturity and gaining a broader range of interests. My biggest win this summer is DS playing for literally hours outside with the neighbor kids, and not just preferred activities but (sometimes) what the other kids want to do. As he has gotten older I let him engage in the preferred activities (hoses/sprinklers; Ipad; TV) but I put a time limit on it so he has no choice but to move on and modify his activities.